1. Field of the Invention
The present invention relates to signal processing and, more specifically but not exclusively, to linearizing non-linear systems, such as linearizing non-linear amplifiers using digital pre-distortion.
2. Description of the Related Art
Modern wireless communications systems require transmitters with a high degree of linearity in order not to interfere with other systems that occupy adjacent radio frequencies. In order to achieve high power efficiency, however, power amplifiers are operated close to saturation where the output is highly non-linear.
In many wireless communication systems, the transmitted RF signal is generated by applying a digital input signal to a sequence of processing that includes digital pre-distortion (DPD), followed by digital-to-analog (D/A) conversion, followed by analog upconversion from baseband or an intermediate frequency (IF) to a radio frequency (RF) prior to transmission, followed by non-linear power amplification, where the DPD processing is intended to compensate for non-linearities in the rest of the processing sequence, especially non-linearities in the amplifier that performs the power amplification.
In such a conventional DPD-based amplifier system, a portion of the RF output signal generated at the amplifier is periodically tapped, downconverted from RF, digitized, and demodulated to form a complex, digital feedback signal that is compared to the complex, digital input signal to characterize the existing distortion in the RF output signal and adjust the DPD processing to attempt to compensate for that distortion. Adjusting the DPD processing is typically implemented by performing certain calculations to update one or more look-up tables (LUTs) that represent the pre-distortion needed to compensate for the distortion in the RF output signal. These LUTs are then used to pre-distort the digital input signal until the next periodic update is performed. To avoid introducing noise into the LUTs, the tapped portion of the RF output signal needs to contain a large number of samples so that the random fluctuations can be made negligible by averaging. For example, in a conventional wireless communication system that generates an RF output signal with a bandwidth of 15 MHz, each tapped portion of the RF output signal is typically about 100 microseconds long, and the LUTs are typically updated once every 10 to 100 milliseconds.
Before the digital feedback signal is compared to the digital input signal, the two signals are typically aligned in both time and phase. These time and phase alignments are typically performed in the digital domain within the same digital processor that performs the DPD processing. For the rest of this specification, in the context of processing designed to update the DPD LUTs, the input signal will be referred to as the “reference” signal to which the feedback signal gets compared.
In particular, time alignment is achieved by shifting in time either the reference signal or the feedback signal so as to minimize, in a least-squares sense, the difference between (i) the power (or, alternatively, the amplitude) of the digital feedback waveform corresponding to the current tapped portion of the RF output signal and (ii) the power (amplitude) of a corresponding waveform of the digital reference signal. Similarly, phase alignment is achieved by shifting the phase of one of the two waveforms so as to minimize, in a least-squares sense, the sum of the squares of the differences between (i) the complex (i.e., in-phase (I) and quadrature-phase (Q)) components of the digital feedback waveform corresponding to the current tapped portion of the RF output signal and (ii) the complex components of the corresponding (i.e., time-aligned) digital reference waveform.
Operationally, time alignment is first performed between the two signals over the entire duration of the tapped portion (i.e., at the waveform level). Then, phase alignment is performed between the resulting time-aligned waveforms over that same entire duration (i.e., at the waveform level). Time alignment is performed to adjust for the delays that occur in both the transmit chain and in the feedback chain. Phase alignment is performed because, in addition to the phase variation introduced by the AM-PM (amplitude modulation to phase modulation) distortion of the amplifier, there is an arbitrary phase difference between the reference and feedback waveforms, which needs to be removed before the waveforms are compared to extract the AM-PM distortion. Ideally, this phase difference is constant for the duration of the feedback waveform, in which case, the phase difference can be removed by multiplying the feedback waveform with a complex number whose value is chosen to minimize the difference between the reference and feedback waveforms in a least squares sense or other suitable measure.
The following Equation (1) represents a closed-form expression for a complex multiplier M that aligns the phase (and also the magnitude) of a sequence of waveform samples tapped from the time-aligned RF output signal with the corresponding sequence of samples from the time-aligned digital reference waveform:M=(C′*R)/(C′*C),  (1)where C is the sequence of complex samples (I+jQ) corresponding to the time-aligned feedback waveform in the form of a column vector, R is the corresponding sequence of complex samples of the time-aligned reference waveform also in the form of a column vector, and C′ is the transpose of C. The symbol * in Equation (1) signifies matrix multiplication.
The phase- and time-aligned version of the feedback waveform is given by the following Expression (2):M*C,  (2)where the symbol * in Equation (2) signifies element-by-element multiplication, since M is a single complex number.